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Geomag Weights and Measures
Quick Reference Dimensions Rod Length A Geomag Rod is 27.00mm long, and has a maximum diameter of 7.40mm. The spheres are 12.70mm in diameter. With use the rods may become slightly compressed, by about 0.1mm. Dimple Depth When connecting a sphere to a rod, the steel sphere impinges past the extreme edges of the cylinder giving rise to what Karl Horton terms the "dimple depth". Since the rod is 27.00mm long and the sphere (a 1/2" ball bearing) is 12.70mm, the ''dimple depth is : \frac{2\times27.00\mbox{mm} + 12.70\mbox{mm} - 65.84\mbox{mm}}{2}=0.43\mbox{mm} Shoulder depth Distance that the magnet is recessed into the housing Air gap The distance between the ball surface and the magnet surface in a joined rod and sphere. (TODO: it's about 1/1000" find experiment data) If I were writing marketing blurb, I'd term this air gap "the genius of Geomag", because it allows the rods and spheres to be repeatedly assembled and broken apart without damage. Naked neodymium magnets and nickel-plated steel balls stick together well, but they tend to damage each other. Weights Rod 4.7g Sphere 8.6g Triangle Panel: Square Panels 1.82g Pentagon Panel Diamond Panel Joint Strength Some actual experiments needed here: 4Newtons approx. --Karl Horton built long chains rod-sphere-rod-sphere and got to 9 feet long before collapse - say 65 rods - that's about 850g (2lb). --http://geomag.kockopes.cz/2008/01/30/how-much-you-can-carry-on-one-rod has tried to measure how much you can carry on one single rod - final result 740g (1.63lb) carried by one single rod. rod-sphere-rod - basic joint sphere-rod-sphere-rod-sphere - suspect that this will be slightly stronger rod-sphere-sphere-rod ultra-joints: multiple north poles on a ball. Rod to Sphere ratio Ever had a big clump of destroyed model in your hands and wondered 'How much is here?' Well, if you had a pair of kitchen scales to hand, and knew the typical sphere to rod ratio for models, you could approximate. Geomag ships rods and spheres in sets with rods and spheres in the ratio two to one, but most people find they never run out of spheres. A typical usage density is three rods for every sphere. For this reason most people stop counting spheres and just consider rods. Rods also account for 90% of the cost of a Geomag set. Examples * Octet Truss (6) Face Centered Cubic close pack: each cubic cell is an octahedron with eight tetrahedral spikes. (TODO: geomag model of stella octangula) 6 octahedron spheres at face centers, 12 tetrahedron spheres at corners, so we need 4*N total spheres. Similarly we have 36 rods - 12 octahedral - not shared, and 24 tetrahedral, each shared amongst 2 implies 24*N rods. Net ratio 6:1. This is the densest packing possible. * 3D Square Lattice (3) How about a lattice of cubes? In this case for each cube you need 8 spheres and 12 rods. Each sphere is shared amongst eight cubes, and each rod by four cubes. So for a cubic lattice with N cubes, you need N spheres and 3N rods, the ratio is 3:1. * Triangular 2D Lattice (3) Think of building a large lattice of triangles: for each triangle you need three spheres and three rods, but each sphere is shared amongst six triangles, but each rod is shared between only two trianges. The ratio here is 3:1. * Checkerboard (2) Checkerboard - model for panels - N spheres 2*N rods ratio 2:1 * Hexagonal Lattice (1.5) Each sphere sees 3 rods so ratio is 3:2 * Necklace (1) An infinite line of rods and balls is the limiting case necklace - 1:1 Category:General Info